Question: Simplify the following expression: $ p = \dfrac{8n - 9}{2n} - \dfrac{10}{3} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{8n - 9}{2n} \times \dfrac{3}{3} = \dfrac{24n - 27}{6n} $ Multiply the second expression by $\dfrac{2n}{2n}$ $ \dfrac{10}{3} \times \dfrac{2n}{2n} = \dfrac{20n}{6n} $ Therefore $ p = \dfrac{24n - 27}{6n} - \dfrac{20n}{6n} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{24n - 27 - 20n }{6n} $ Distribute the negative sign: $p = \dfrac{24n - 27 - 20n}{6n}$ $p = \dfrac{4n - 27}{6n}$